"It would be great to see (Federal Opposition Leader) Tony Abbott showing the same leadership on this reform as a conservative leader.

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"It is embarrassing that Australia now continues to fall behind the rest of the English-speaking world when it comes to marriage equality.

"I would also say that the vote in the UK proves that civil unions are a failed experiment and that you can't give equality a different name."

Mr Greenwich, who married his partner in Argentina last year, said the debate in NSW was progressing well.

"In NSW the debate is at a very exciting stage, we have people from all parties now working together to progress the reform," he said.

"The community needs to continue to be strong and vocal on this reform."

The NSW cross party working group for marriage equality said the UK bill would mean same-sex couples in Australia, where one had British citizenship, would now be able to get married in the British Consulate in Sydney.

Gay couples living in NSW under a UK civil partnership would also be able to convert their civil partnership to marriage at the consulate, the group said.